1+Zm 9 n, m € Z}1+2n1- Prove that if (Q -(0),) is a group, and H = {1+2mis a subset of Q - {0}., then prove that (H.) is a subgroup of(Q - (0),).

A subset H of a group G, · is said to be a subgroup of G, · if for any a,b∈H we have: a·b∈H a-1∈H…

Answered: 1- Prove that if (Q -(0),) is a group,…

1- Prove that if (Q -(0),) is a group, and H = an, m e Z} 1+2m is a subset of Q - {0)}, then prove that (H.) is a subgroup of (Q - (0),).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 9E: 9. Suppose that and are subgroups of the abelian group such that . Prove that .

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Question

1+Zm 9 n, m € Z}
1+2n
1- Prove that if (Q -(0),) is a group, and H = {
1+2m
is a subset of Q - {0}., then prove that (H.) is a subgroup of
(Q - (0),).

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